Therefore, we are faced with the following possibilities:
* You believe in God.
o If God exists, you go to heaven: your gain is infinite.
o If God does not exist, your loss (the investment in your mistaken belief) is finite and therefore negligible.
* You do not believe in God.
o If God exists, you go to hell: your loss is infinite and your gain is zero.
o If God does not exist, your gain is finite and therefore negligible.
With these possibilities, and the principles of statistics, Pascal hoped to have demonstrated that the only prudent course of action is to believe in God. It is a simple application of game theory (to which Pascal had made important contributions).
Another way of portraying the Wager is as a decision under uncertainty with the values of the following decision matrix:
God exists (G) God does not exist (~G)
Belief in God (B) +∞ (heaven) −N (finite)
Non-belief in God (~B) −∞ (hell) +M (finite)